Cost-Effectiveness Acceptability Curve Plots

Introduction

The intention of this vignette is to show how to plot different styles of cost-effectiveness acceptability curves using the BCEA package.

Two interventions only

This is the simplest case, usually an alternative intervention (\(i=1\)) versus status-quo (\(i=0\)).

The plot show the probability that the alternative intervention is cost-effective for each willingness to pay, \(k\),

\[ p(NB_1 \geq NB_0 | k) \mbox{ where } NB_i = ke - c \]

Using the set of \(N\) posterior samples, this is approximated by

\[ \frac{1}{N} \sum_j^N \mathbb{I} (k \Delta e^j - \Delta c^j) \]

R code

To calculate these in BCEA we use the bcea() function.

data("Vaccine")

he <- bcea(eff, cost)
#> No reference selected. Defaulting to first intervention.
# str(he)

ceac.plot(he)

The plot defaults to base R plotting. Type of plot can be set explicitly using the graph argument.

ceac.plot(he, graph = "base")

ceac.plot(he, graph = "ggplot2")

# ceac.plot(he, graph = "plotly")

Other plotting arguments can be specified such as title, line colours and theme.

ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(color = "green"),
          theme = theme_dark())

Multiple interventions

This situation is when there are more than two interventions to consider. Incremental values can be obtained either always against a fixed reference intervention, such as status-quo, or for all pair-wise comparisons.

Against a fixed reference intervention

Without loss of generality, if we assume that we are interested in intervention \(i=1\), then we wish to calculate

\[ p(NB_1 \geq NB_s | k) \;\; \exists \; s \in S \]

Using the set of \(N\) posterior samples, this is approximated by

\[ \frac{1}{N} \sum_j^N \mathbb{I} (k \Delta e_{1,s}^j - \Delta c_{1,s}^j) \]

R code

This is the default plot for ceac.plot() so we simply follow the same steps as above with the new data set.

data("Smoking")

he <- bcea(eff, cost, ref = 4)
# str(he)
ceac.plot(he)


ceac.plot(he,
          graph = "base",
          title = "my title",
          line = list(color = "green"))

ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(color = "green"))

Reposition legend.

ceac.plot(he, pos = FALSE) # bottom right

ceac.plot(he, pos = c(0, 0))

ceac.plot(he, pos = c(0, 1))

ceac.plot(he, pos = c(1, 0))

ceac.plot(he, pos = c(1, 1))

ceac.plot(he, graph = "ggplot2", pos = c(0, 0))

ceac.plot(he, graph = "ggplot2", pos = c(0, 1))

ceac.plot(he, graph = "ggplot2", pos = c(1, 0))

ceac.plot(he, graph = "ggplot2", pos = c(1, 1))

Define colour palette.

mypalette <- RColorBrewer::brewer.pal(3, "Accent")

ceac.plot(he,
          graph = "base",
          title = "my title",
          line = list(color = mypalette),
          pos = FALSE)


ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(color = mypalette),
          pos = FALSE)

Pair-wise comparisons

Again, without loss of generality, if we assume that we are interested in intervention \(i=1\), then we wish to calculate

\[ p(NB_1 = \max\{NB_i : i \in S\} | k) \]

This can be approximated by the following.

\[ \frac{1}{N} \sum_j^N \prod_{i \in S} \mathbb{I} (k \Delta e_{1,i}^j - \Delta c_{1,i}^j) \]

R code

In BCEA we first we must determine all combinations of paired interventions using the multi.ce() function.

he <- multi.ce(he)

We can use the same plotting calls as before i.e. ceac.plot() and BCEA will deal with the pairwise situation appropriately. Note that in this case the probabilities at a given willingness to pay sum to 1.

ceac.plot(he, graph = "base")


ceac.plot(he,
          graph = "base",
          title = "my title",
          line = list(color = "green"),
          pos = FALSE)


mypalette <- RColorBrewer::brewer.pal(4, "Dark2")

ceac.plot(he,
          graph = "base",
          title = "my title",
          line = list(color = mypalette),
          pos = c(0,1))

ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(color = mypalette),
          pos = c(0,1))

The line width can be changes with either a single value to change all lines to the same thickness or a value for each.

ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(size = 2))

ceac.plot(he,
          graph = "ggplot2",
          title = "my title",
          line = list(size = c(1,2,3)))